VAR of Long & Short European Call Options


I have over 1000 simulated stock prices for an option that is expiring in 3 months. I have calculated the EU call option payoff of 1000 simulated prices and now I have 1000 simulated payoffs of call. I am looking to calculated the VaR of Long and short call but without the delta approach. I know how to estimate VAR of stocks (Standard devaition * Z-score). How do I estimate 95% VAR for call options?

Thank you!

Disclaimer of this is out of my area of expertise, so I wouldn’t recommend actually implementing anything I suggest here.

I believe you can compute VAR based on the results of a simulation. For example if you want a 95% VAR you find the worst 5% of the outcomes for you and the outcome that is the best (of that worst 5%) is your VAR. Since you have stock prices, I would think you could just compute the option payoff given each of those stock prices and then use the method above to compute a simulated VAR.

I hope someone with more expertise in this area than myself answers this, because I’m definitely interested and following.

Again don’t actually do this until you here from someone who knows more about this than myself